OK.
Power is a measure of how much work (as in F*D) you can due per unit time (as in seconds) a great way of showing what power is, is that 1 Watt is equal to 1 Joule per Second.
Does anyone disagree with that?
From that we can conclude that if you have more power (say 2 Watts) you can either do the same amount of work in less time (1 Joule per 1/2 second), or you can do more work in the same time (2 Joules per second).
Does anyone disagree with that?
Now to accelerate you need to change the velocity of the fixed weight vehicle. To increase velocity you need to add more kinetic energy (that would be Joules again) To be an acceleration there needs to be a time constraint (it can't take forever to get there (to the target speed) unless you are trying to go as fast as light). So now we can conclude that acceleration is equal to the rate you can supply the neccessary energy (in Joules) per unit time (in seconds)
So Power is what accelerates you.
Now here is what is confusing you: Torque is the force at the wheels (remember work is F*D) that gets things moving. The Force created is equal to the torque at the wheels divided by the dynamic radius. The Torque at the wheels is equal to the Power at the wheels divided by the angular speed of the wheels (so you don't need to know the gearbox ratio if you now the angular speed of the wheel which is easily calculated if you know the speed and the radius of the wheel).
So... Torque from the engine is not important on it's own... The power curve is what everyone should be focusing on (not just peak power but the whole curve).
In the end Power has all the torque in it
Torque doesn't have any power in it.
Power, whether measured as HP, PS, or KW is what accelerates cars and gets it up to top speed. Power also determines how far you take a wall when you hit it
Engine torque is an illusion.